Abstract:
In this paper, we prove that the Boundary Condition Constants for the Boundary Value Problem
π : ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
4
(1)
3
(2)
2
(4)
Lφ ≡ φ x + P x φ x + P x φ x + P x φ x = λφ x
{ ( ) ( )} 0
4
1
( 1) ( 1)
≡ ∑ + =
=
− −
s
s
rs
s
Urφ mrsφ a n φ b (1≤ r,s ≤ 4)
can be replaced by Boundary Condition Functions and that the Boundary
Condition Functions are asymptotically equivalent for large values of λ , to the
Boundary Condition Functions for the corresponding Fourier problem �, given
by
π
F
: ( ) ( )
(4)
x = λφ x
{ ( ) ( )} 0
4
( 1) ( 1)
≡ ∑ + =
− −
s
rs
s
Urφ mrsφ a n φ b (1≤ r,s ≤ 4)
